The relative performance of a non-linear FAS multigrid algorithm and an equivalent linear multigrid algorithm for solving two di erent non-linear problems is investigated. The rst case consists of a transient radiation-di usion problem for which an exact linearization is available, while the second problem involves the solution of the steady-state Navier-Stokes equations, where a rst-order disc...

This paper investigates the polytope associated with the classical standard linearization technique for the unconstrained optimization of multilinear polynomials in 0-1 variables. A new class of valid inequalities, called 2-links, is introduced to strengthen the LP relaxation of the standard linearization. The addition of the 2-links to the standard linearization inequalities provides a complet...

Abstract In this paper, we propose an efficient approach to solve the fifthorder KdV equations. By using the variational iteration method, the exact solutions of the fifth-order KdV equations are given without the calculation of the complicated Adomian’s polynomials, linearization, discretization, weak nonlinearity assumptions or perturbation theory. Numerical examples are presented that show t...

The increasing share of volatile renewable electricity production motivates demand response. Substantial potential for response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization schedules can exploit the potential, but leads to numerically challenging problems nonlinear dynamic processes. In this paper, we propose capture process dynamics us...

The exact solution of the reliability of structures under stochastic loading is generally difficult, and various approximate methods have been developed. The most popular are the linearization method, the Monte-Carlo method and its numerous variants. In this paper new modification of the Monte-Carlo method based on asymptotical expansion is examined. Results of mathematical simulation are given.

We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they preserve the linearization of the original system at every point. In particular, locally exact integrators preserve all fixed points and are A-stable. We apply this approach to popular schemes including Euler schemes, impl...